Down or Out: Assessing the Welfare Costs of Household Investment Mistakes

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1 Down or Out: Assessing the Welfare Costs of Household Investment Mistakes Laurent E. Calvet Imperial College London, HEC Paris, and National Bureau of Economic Research John Y. Campbell Harvard University and National Bureau of Economic Research Paolo Sodini Stockholm School of Economics and Sveriges Riksbank This paper investigates the efficiency of household investment decisions using comprehensive disaggregated Swedish data. We consider two main sources of inefficiency: underdiversification ( down ) and nonparticipation in risky asset markets ( out ). While a few households are very poorly diversified, most Swedish households outperform the Sharpe ratio of their domestic stock index through international diversification. Financially sophisticated households invest more efficiently but also more aggressively, and overall they incur higher return We thank Statistics Sweden for providing the data. We received helpful comments from Monika Piazzesi (the editor), Nick Barberis, Gene Fama, Luigo Guiso, Tor Jacobson, Matti Keloharju, Francis Kramarz, Massimo Massa, Bruno Solnik, Tuomo Vuolteenaho, three anonymous referees, and seminar participants at Bocconi, Centre de Recherche en Economique et Statistiques, Gerzensee, Harvard, Imperial College, New York University, Riksbank, the University of Chicago, the University of Frankfurt, the University of Stockholm, the University of Vienna, Wharton, Yale, the 2006 Centre for Economic Policy Research Adam Smith Asset Pricing Conference, the 2006 Western Finance Association, the 2006 NBER Summer Institute, and the 2007 Bank of Spain Conference on Household Finances. The project benefited from excellent research assistance by Daniel Sunesson. This material is based on work supported by the Agence Nationale de la Recherche under a Chaire d Excellence to Calvet, Bankforskningsinstitutet under a research grant to Sodini, the HEC Foundation, the National Science Foundation under grant to Campbell, Riksbank, and the Wallander and Hedelius Foundation. [ Journal of Political Economy, 2007, vol. 115, no. 5] 2007 by The University of Chicago. All rights reserved /2007/ $

2 708 journal of political economy losses from underdiversification. The return cost of nonparticipation is smaller by almost one-half when we take account of the fact that nonparticipants would likely be inefficient investors. I. Introduction Modern financial markets offer a rich array of investment opportunities. Households in developed countries can accumulate liquid wealth in bank accounts, money market funds, bond funds, equity mutual funds, individual bonds and equities, financial products with insurance features such as annuities and capital insurance funds, and derivative securities. In addition, many households have significant wealth in less liquid forms such as real estate and private businesses. How do households exploit these investment opportunities? Do they typically follow the precepts of standard financial theory such as participation (taking at least small amounts of compensated risk) and diversification (avoiding uncompensated risk)? To the extent that they deviate from these precepts, are the costs of such deviation modest and therefore explicable by relatively small frictions ignored in standard theory, or are they large and accordingly hard to rationalize? How heterogeneous are household investment strategies? Are cross-sectional differences in investment strategies correlated with observable household characteristics such as age, education, and wealth? These questions are of central importance in economics and finance, but reliable answers are extremely hard to obtain because they require a high-quality data set on investment strategies. To study household portfolios, we would like to have data with at least four characteristics. First, the data should include a representative sample of the population. Second, for each household, the data should measure both total wealth and an exhaustive breakdown of wealth into relevant categories. Third, these categories should be detailed enough to distinguish between asset classes, and for some issues notably the question of diversification we would like to observe holdings of individual assets. Finally, the data must be accurately reported. In this paper we use Swedish government records to construct a panel of wealth and income data covering all Swedish households over the period These data are available because Sweden levies a wealth tax. In order to collect this tax, the government assembles records of financial assets, including mutual funds, that are held outside defined contribution pension accounts. The records go down to the individual security level and are based on statements from financial institutions that are verified by taxpayers. The data set also provides information on real estate holdings and the income, demographic composition, ed-

3 household investment mistakes 709 ucation, and location of all households. For nonretirement wealth, which accounts for 84 percent of aggregate household financial wealth in 2002, our data set meets the four criteria listed above, giving us the unique opportunity to analyze the financial behavior of the entire population of an industrialized country. We study the stocks, mutual funds, and cash held by Swedish households outside defined contribution pension accounts. Using the return histories of these assets, we estimate the total risk and systematic risk of each household portfolio within a mean-variance framework. Our measure of systematic risk is covariance with a global equity index. To the extent that stock returns are well described by a global capital asset pricing model (CAPM), our risk estimates can be used to estimate the means of Swedish household portfolio returns. We obtain four main results. First, the median household portfolio has a mean return close to the maximum that is achievable given its standard deviation. Equivalently, its Sharpe ratio, its mean excess return over cash divided by its standard deviation, is close to the maximum level attained by a global equity index; and its return loss, the difference between its mean return and the maximum consistent with its standard deviation, is small. Earlier researchers such as Blume and Friend (1975), Kelly (1995), and Goetzmann and Kumar (2004) have found that households own severely underdiversified portfolios of individual stocks; but we show that mutual funds and cash dominate direct stockholdings in many household portfolios, limiting the return losses from concentrated stock portfolios. A majority of participating households actually outperform the Sharpe ratio of their domestic market, which can be explained by the substantial share of international securities in popular mutual funds. This finding is robust to the use of alternative asset pricing models. Second, there is significant cross-sectional variation in the efficiency of equity investment, as measured by the Sharpe ratios of household portfolios, and in the return losses from underdiversification. At the ninety-fifth percentile of the return loss distribution, losses are large whether they are measured relative to the size of the portfolio, in dollars, or as a fraction of disposable income. Thus a minority of Swedish households do appear to be severely underdiversified. Third, households with greater financial sophistication, as measured for instance by wealth or education, tend to invest more efficiently but also more aggressively. Their portfolios have higher Sharpe ratios but also higher volatility. As a result, sophistication generally has an ambiguous effect on the average return loss. In Sweden, we find that the average return loss from underdiversification is larger for more sophisticated households. Fourth, measures of financial sophistication also predict the proba-

4 710 journal of political economy bility that a household will participate in the equity market. Households with low education and wealth are less likely to participate and more likely to invest inefficiently if they do participate. This result suggests that nonparticipating households would likely invest poorly if they entered risky asset markets. We show that the welfare costs of nonparticipation are lower by almost one-half when underdiversification costs are taken into account. Agents who are out might well be down if they entered financial markets. Some of our results confirm earlier empirical findings on individual portfolios. Consistent with the results of Heaton and Lucas (2000), we find that Swedish households exposed to more background risk, such as entrepreneurs or large families, tend to invest less aggressively and more efficiently. Similarly, our finding that richer households attain higher Sharpe ratios seems consistent with earlier research documenting a positive correlation between rationality and wealth (Vissing-Jorgensen 2004). Our data set has significant advantages relative to previously available data. Most work on household portfolio choice relies on surveys, such as the widely used U.S. Survey of Consumer Finances (SCF). 1 The SCF is representative and measures all components of wealth, but it reports holdings of broad asset classes rather than specific financial assets, and it relies on the accuracy of voluntary household reporting. The Swedish data cover individual financial assets, reported by financial institutions and confirmed by taxpayers, who are subject to legal penalties for inaccurate reporting. Following the pioneering work of Schlarbaum, Lewellen, and Lease (1978) and Odean (1998, 1999), a number of authors have looked at the account records of individual investors reported by a brokerage house. 2 These brokerage records are highly accurate reports of holdings and trades in individual stocks, but they sample customers of the brokerage house rather than the entire population and do not necessarily represent total wealth even of these customers, who may also have other 1 Recent studies that use the SCF include Heaton and Lucas (2000), Poterba and Samwick (2001), Tracy and Schneider (2001), Bertaut and Starr-McCluer (2002), Carroll (2002), and Bergstresser and Poterba (2004). Other surveys of wealth are the Wharton survey conducted in the 1970s (Blume and Friend 1978) and the UBS/Gallup survey (Vissing-Jorgensen 2004; Graham, Harvey, and Huang 2005), both of which rely on telephone interviews, and the Health and Retirement Survey (Juster, Smith, and Stafford 1999), which has high-quality data but only on older households. 2 Recent papers using brokerage house data include Barber and Odean (2001), Zhu (2002), Goetzmann and Kumar (2004), Ivković and Weisbenner (2005), and Ivković, Sialm, and Weisbenner (2007).

5 household investment mistakes 711 accounts elsewhere. Similar difficulties afflict registries of ownership (e.g., Grinblatt and Keloharju 2000) and recent studies of asset allocation in 401(k) accounts and other tax-favored retirement accounts. 3 Some other work has been done using government tax records. The U.S. tax system requires reporting of wealth only in connection with the estate tax, which is levied only on the holdings of the very rich at the date of death. Blume and Friend (1978) and Kopczuk and Saez (2004) have used U.S. estate tax records to study household asset allocation, but it is hard to know how to extrapolate from wealthy and elderly households to the broader population. Massa and Simonov (2006) have also studied the portfolios of Swedish households. Massa and Simonov do not make direct use of Swedish government records. Instead, they begin with an income and wealth survey, Longitudinal Individual Data for Sweden (LINDA), which describes a representative sample of about 3 percent of the Swedish population. LINDA contains high-quality data on income, real estate, and overall taxable wealth but gives limited information about the components of financial wealth. Only the share of each household s wealth invested in risky assets and its bank account balance are available. Massa and Simonov merge LINDA with a data set on individual stock ownership of Swedish companies from 1995 to Stock ownership data were available in this period since Swedish companies were legally required to report the identity of most of their shareholders. These reporting requirements did not apply to mutual funds or to bond issuers, and thus Massa and Simonov cannot measure bond or mutual fund holdings. Their data set, like the brokerage records used by Odean (1998, 1999), can be used to measure biases in households decisions with respect to individual stocks, but not the overall degree of diversification in household portfolios. The article is organized as follows. Section II presents the data and describes asset allocation at the aggregate and household levels. Section III investigates the diversification of Swedish household portfolios, using a mean-variance framework. Section IV relates portfolio efficiency to household characteristics, Section V derives implications for the welfare cost of nonparticipation, and Section VI presents conclusions. The online Appendix describes our methods in greater detail. 3 Recent studies of such accounts include Benartzi and Thaler (2001), Madrian and Shea (2001), Choi et al. (2002, 2004), Agnew, Balduzzi, and Sundén (2003), and Ameriks and Zeldes (2004).

6 712 journal of political economy II. Household Asset Allocation A. Data Summary To understand our data set, it is helpful to begin with a brief description of the Swedish economy and tax system. Sweden is an industrialized nation with a population of almost 9 million. The GDP per capita in 2002 is estimated at $27,300 when currencies are converted at purchasing power parity; this is slightly higher than the EU average of $26,000. Sweden is characterized by a large middle class, lower inequality in disposable income, and a more progressive tax and transfer system than most other industrialized nations. 4 Swedish households are subject to both a capital income tax and a wealth tax. Capital income (interest, dividends, and capital gains) is taxed at a flat rate of 30 percent, with deductions for interest paid and capital losses. The wealth tax is paid on all the assets of the household, including real estate and financial securities, with the important exception of private businesses and shares in small public businesses. 5 It is levied at a rate of 1.5 percent on taxable wealth above a threshold, which was equal to 2 million Swedish kronor (SEK) for married couples and 1.5 million SEK for single taxpayers in The Swedish krona traded at $ at the end of 2002, so these thresholds correspond to $225,000 for married couples and $170,000 for single taxpayers. In 2002, 263,000 individuals paid a total of $430 million in wealth tax. Because of the existence of the wealth tax, the government s statistical agency, Statistics Sweden (also known by its Swedish acronym SCB), has a parliamentary mandate to collect household-level data on wealth. Statistics Sweden compiles information on household finances from a variety of sources, including the Swedish Tax Agency, welfare agencies, and the private sector. Financial institutions supply information to the tax agency on their customers deposits, interest paid or received, security investments, and dividends. Importantly, nontaxable securities and securities owned by investors below the wealth tax threshold are included. Employers similarly supply statements of wages paid to their employees. In April, taxpayers receive a tax return on which all the data supplied by employers and financial institutions have already been en- 4 For 2002, we obtain a Gini coefficient of 35.0 percent for gross income (before taxes and transfers) and 27.1 percent for disposable income. These coefficients are low by international standards. 5 More precisely, taxable wealth is calculated as 100 percent of the value of bank accounts paying interest above 100 SEK per year, bonds and fixed-income mutual funds, capital insurance products, residential real estate, and cars and boats exceeding 10,000 SEK in value, plus 80 percent of the value of A-list (generally large) Swedish stocks, comparable foreign stocks, and equity mutual funds. We refer the reader to Swedish Tax Agency (2004) for further details.

7 household investment mistakes 713 tered by the tax agency. The taxpayer checks the figures and, if necessary, corrects errors and adds information or claims for deductions. We compiled the data supplied by Statistics Sweden into a panel covering four years ( ) and the entire population of Sweden. The data set includes demographic information such as age, gender, marital status, immigration status, and education, as well as household composition and identification number. All tax returns are filed individually in Sweden since the tax code does not allow the possibility of joint filing. However, the household identification number allows us to group residents by living units and thus investigate finances at the family level. There are about 4.8 million households in Sweden during our sample period. The panel contains highly disaggregated wealth information, which lists the worldwide assets owned by the resident at the end of a tax year. All financial assets must be reported, including bank accounts, mutual funds, and stocks. The information is provided for each individual account or each security referenced by its International Security Identification Number. The database also records contributions made during the year to private pension savings, as well as debt outstanding at yearend and interest paid during the year. We also have disaggregated data on income. For labor income, the database reports gross labor income and business sector. For capital income, the database reports for each bank account or security the income (interest, dividends) that has been earned during the year. In this article we use disposable income, and private pension contributions as a fraction of income, as proxies for financial sophistication. We believe our data to be of unusually high quality since the information comes directly from Swedish firms, financial institutions, and state agencies. The entire population is observed, so selection bias is not a problem. We acknowledge, however, four possible weaknesses in our data set. First, we do not observe the value of households defined contribution pension savings. These include assets in private pension plans and in public defined contribution accounts that were established in a 1999 pension reform. According to official statistics, defined contribution pension savings had an aggregate value of $25.6 billion in Sweden at the end of 2002, whereas aggregate household financial wealth invested outside pension plans amounted to $131.3 billion. Our data set therefore contains 84 percent of household financial wealth. Furthermore, since pension savings are usually invested in mutual funds, their inclusion would likely strengthen our main finding that households are reasonably well diversified. Second, we observe the total value of capital insurance products, a form of tax-favored saving, but we do not observe the allocation of these

8 714 journal of political economy assets. 6 We have made several alternative assumptions about asset allocation in capital insurance and find in the Appendix that our results are robust to any of these assumptions. Third, bank accounts need not be reported to the Swedish Tax Agency unless they receive more than 100 SEK (or $11) in interest during the year. Missing bank account data can distort our estimates of the share held by a household in risky assets but do not affect our estimates of diversification of risky portfolios. As discussed in the Appendix, we have employed several imputation methods to address this problem. Finally, there is the issue of tax evasion, the main form of which is probably the ownership of unreported international assets. We can crosscheck the accuracy of foreign holdings in our data set by comparing the cumulative sum of aggregate investment flows over a long time period. Since 1979, Statistics Sweden has reported two different measures of aggregate household investment: (1) the difference between aggregate disposable income and aggregate consumption (imputed from payroll, sales, tax, and transfer data supplied by firms and government agencies) and (2) the aggregate investment of individuals (reported by financial institutions). The cumulated difference between the first and the second estimates over the period represents about 6.2 percent of the aggregate assets owned by households at the end of The discrepancy is caused by a variety of items, including the consumption of Swedish travelers in foreign countries, capital gains, and unreported foreign investment. This analysis suggests that unreported foreign assets represent a modest fraction of household assets. More generally, illegal foreign investments involve fixed costs and are likely to be significant only for the very rich. B. Aggregate Asset Allocation We report in table 1 the aggregate wealth of households in our data set and its breakdown into main asset categories at the end of Specifically, we compute gross wealth as the nominal value of financial and real estate assets held by the household. Aggregate gross wealth is ap- 6 Capital insurance is a form of investment subjected to a special tax treatment by the Swedish Tax Authority. It exists in two forms: unit link or traditional. Unit link savings are invested in mutual funds. Traditional insurance products guarantee a minimum fixed return, which between 1999 and 2002 could not exceed the 3 percent limit set by the Finance Inspection Board (Finansinspektionen). The taxation of capital insurance is based on the Statslåneränta, which is defined as the average market interest rate on Swedish government bonds with a remaining maturity of at least five years. Swedish authorities use the Statslåneränta as a proxy for the long-run nominal interest rate. Capital insurance accounts are subjected to a flat tax on their market value, whose rate is 27 percent of the Statslåneränta. In 2002, this corresponded to a tax on market value that was slightly higher than 1 percent.

9 household investment mistakes 715 TABLE 1 Aggregate Wealth Statistics (December 31, 2002) Aggregate Holdings (in Billion Dollars) Micro Data (1) Official Statistics (2) Aggregate Asset Allocation (from Micro Data) Wealth Share (3) Financial Share (4) Financial assets: Bank accounts % 35.1% Money market funds % 5.5% Mutual funds % 22.3% Domestic stocks % 20.9% International stocks 2.3 NA.5% 1.8% Capital insurance % 9.2% Bonds and derivatives % 5.2% Total financial assets % 100.0% Real estate: Residential % Nonresidential % Total real estate % Total gross wealth % Total debt Total net wealth Number of households 4,869,448 4,869,448 Gross wealth per household $98,313 $97,692 Net wealth per household $67,966 $67,072 Note. The table reports aggregate wealth statistics for all resident Swedish households on December 31, We convert all financial variables into U.S. dollars using the exchange rate at the end of 2002 (1 SEK p $ ). In col. 1, we aggregate up the value of the asset holdings observed for each household in our micro data set. Column 2 reports the corresponding official statistic published by Statistics Sweden. We compute in col. 3 the asset allocation of the aggregate portfolio of financial and real estate assets in our data set, and in col. 4 the allocation of the financial portfolio alone. proximately $480 billion for the households in our data set. On a per household basis, we estimate gross wealth at about $98,000, debt at $30,000, and therefore net wealth at $68,000. Financial wealth represents 27.5 percent of gross wealth, or about $27,000 per household, and real estate accounts for the remaining 72.5 percent. Financial wealth is decomposed into its main components: bank accounts, money market funds, mutual funds, stocks, capital insurance, and other assets (bonds and derivatives). Cash, which consists of holdings in bank accounts and money market funds, represents 41 percent of financial wealth. Mutual funds, including bond and equity funds, and direct stockholdings account for another 45 percent of financial wealth. The remainder is accounted for by capital insurance products (9 percent) and directly held bonds and derivatives (5 percent). Direct stockholdings account for almost 23 percent of financial wealth. They have a market value of $29.8 billion in our data set and primarily consist of domestic equity ($27.5 billion). Since Swedish stock

10 716 journal of political economy markets had a market capitalization of $201.4 billion at the end of 2002, the domestic investors in our data set owned directly 13.7 percent of Swedish stocks, a figure consistent with the 14.4 percent estimate reported by the Swedish Central Bank. 7 Foreign stocks play a minor role, with direct holdings of about $2.3 billion. This finding is consistent with the relatively high cost of trading individual foreign stocks. International diversification, however, is readily available to Swedish investors through mutual funds, which account for 22 percent of financial wealth. Swedish financial institutions have long recognized the importance of international diversification and routinely offer their customers a wide range of corresponding products. For instance, the most popular risky mutual fund in Sweden, Robur Bank s Kapitalinvest, holds half of its assets in foreign stocks. Other very popular funds, such as SHB s Sweden/World or SEB s Aktieparfond, also invest substantially in international equity. These funds make it straightforward for middleclass Swedish households to achieve a good level of international diversification. We investigate in Section III whether households take advantage of these opportunities. Table 1 also includes the official wealth statistics computed by Statistics Sweden. Our data set matches these official statistics remarkably well. Statistics Sweden reports aggregate financial wealth equal to $131.3 billion, which is very close to our $131.7 billion estimate. The aggregate estimates are also quite close for each category of assets. The main differences occur for mutual funds and money market funds. We attribute this discrepancy to slightly different fund classifications. 8 The aggregated holdings in both types of funds are $36.1 billion with the SCB data and $36.6 billion with our data. Our data set thus has good aggregation properties, which confirms its reliability and accuracy. C. Asset Allocation in the Cross Section Aggregate statistics tell us how the average dollar of wealth is allocated. This can be quite different from the asset allocation of the average household, however, because the wealthy invest differently than poorer 7 In table 1, domestic equity consists of all the publicly traded companies that are registered in Sweden. This definition excludes transnational companies, such as ABB or Astra Zeneca, which have important operations in Sweden, are traded in Swedish stock markets, and are included in the domestic indexes. When these companies are included in the definition of domestic equity, household direct investments in domestic stocks have an aggregate value of $29.74 billion at the end of 2002, which represents 14.8 percent of Swedish stocks. The Central Bank estimate of direct domestic stockholdings (14.4 percent) is thus contained between the low (13.7 percent) and high (14.8 percent) estimates from our data set. 8 We characterize a fund as a money market fund if the standard deviation of its returns is less than 0.35 percent per year. This cutoff corresponds to a substantial gap in the distribution of historical standard deviations and a shift in the names of the funds.

11 household investment mistakes 717 Fig. 1. Composition of the financial portfolio. The figure represents the cross-sectional distribution of the asset allocation in the financial portfolio owned by Swedish households at the end of We subdivide households into gross wealth percentiles and report the average asset share within each wealth group. Households in the lowest two deciles are not shown in the figure because their total wealth is poorly measured and they hold almost nothing but cash. households (Heaton and Lucas 2000; Tracy and Schneider 2001; Carroll 2002). A detailed microeconomic analysis is required to obtain a good picture of investment patterns at the household level. Figure 1 illustrates how the composition of the financial portfolio varies with gross wealth. The horizontal axis shows percentiles of the distribution of gross wealth, starting at the twentieth percentile because the poorest 20 percent of Swedish households have almost no measurable wealth given the nonreporting of small bank accounts. The shares of all risky assets increase quickly between the twentieth and thirtieth percentiles and then become relatively stable until the ninetieth percentile. Mutual funds represent the largest fraction of risky assets held by households in this region of the wealth distribution. In the highest decile, however, direct stockholdings have a quickly increasing share and end up representing more than half of financial wealth for the richest Swedish households. Thus while stocks and mutual funds represent comparable fractions of aggregate wealth, figure 1 illustrates that mutual funds dominate stocks in most household portfolios. The wealth composition of Swedish households is consistent with results reported for other industrialized countries such as the United States (Bertaut and Starr-McCluer 2002).

12 718 journal of political economy Although our data can be used to examine many aspects of household finance, in this article we concentrate on diversification within portfolios of stocks, mutual funds (including both bond and equity funds), and cash (including both bank accounts and money market funds). We consider these portfolios in isolation and measure their risks using a meanvariance approach. We exclude capital insurance products because our database contains their total value but not their asset allocation. We have checked in the online Appendix that our diversification results are robust to including capital insurance products with a range of reasonable assumptions about their asset allocation. Our data could also be used to study the risks of labor income, real estate, and directly held bonds and derivatives jointly with the risks we consider. However, this would pose significant measurement challenges because the capitalized value of labor income is not directly observed, the value of real estate is measured imperfectly and infrequently, and bonds and derivatives are numerous, sometimes short-lived, and frequently illiquid. Even excluding these other assets, we believe that meanvariance analysis is informative about diversification within households equity and mutual fund portfolios. In principle, undiversified portfolios could be used to hedge specific risks in income or real estate, but previous research has found little evidence of this behavior. Notably, Massa and Simonov (2006) have investigated income hedging using data on direct stockholdings of Swedish households, and they find no evidence of hedging behavior except among the richest Swedish households. The main difference between their data set and ours is that we measure mutual fund holdings, which seem less suitable for income hedging than the direct stockholdings examined by Massa and Simonov. In the remainder of the article we present a cross-sectional analysis for a random subsample that initially contains 100,000 households, or slightly more than 2 percent of the Swedish population, at the end of From the initial set of 100,000 households, we exclude those that have extremely low income or financial wealth (0.4 percent of the sample) or hold unusually short-lived assets whose risk properties are difficult to measure accurately (1.6 percent of the initial sample). 9 In the online Appendix we check that our results are robust to the inclusion of those investors. For each household, we consider three types of portfolios: the complete portfolio, which contains all the stocks, mutual funds, and cash owned by the household; the risky portfolio, which contains stocks and risky mutual funds but excludes cash; and the stock portfolio, which contains 9 Specifically, we exclude those whose average reported disposable income over the past three years is less than 1,000 SEK ($113), whose reported financial wealth is less than 3,000 SEK ($339), or whose portfolios include assets for which we have fewer than 24 return observations through 2004.

13 household investment mistakes 719 direct stockholdings but excludes equity owned through mutual funds. The complete portfolio tells us the overall amount of risk taken by the household; the risky portfolio allows us to decompose the risk the household takes; and the stock portfolio allows us to compare our results with those of Goetzmann and Kumar (2004), who observe only directly held stocks and not mutual funds. We find that 87 percent of households that hold risky mutual funds or stocks own mutual funds, whereas 55 percent are direct stockholders. Furthermore, 76 percent of direct stockholders also own mutual funds. These facts imply that mutual funds play a key role in household diversification. In table 2, we report summary statistics for these portfolios as well as other household characteristics in our subsample. A household is viewed as a participant in risky asset markets if its risky portfolio share is positive. A participating household takes financial risk and can make diversification mistakes. With this definition, 62 percent of Swedish households were participants at the end of Average financial wealth is substantially higher for participants ($41,000) than for nonparticipants ($8,000). We also observe that for participants, the average value of the complete portfolio we consider is about $35,000 as compared to $41,000 if we were to include capital insurance, directly held bonds, and derivatives. III. Diversification of Household Portfolios We now ask how households take risk within their portfolios. We begin by investigating portfolio variance, then assume an asset pricing model and use it to conduct a mean-variance analysis at the household level. A. Idiosyncratic and Systematic Risk We observe at the end of year t the portfolio of financial assets owned by household h. Let q h denote the corresponding vector of portfolio weights. The portfolio generates a random return between the end of year t and the next time the portfolio is rebalanced. Since we do not observe rebalancing within the year, we cannot directly compute household portfolio returns. For this reason, we investigate the properties of household portfolios by estimating the moments of asset returns and then inferring the household portfolio characteristics. We begin by presenting results that impose no restriction on the mean returns of stocks and mutual funds. The risk-free rate in Sweden is proxied by the yield on the one-month Swedish Treasury bill. Excess returns are computed for all assets at a monthly frequency in local currency. We estimate the variance-covariance matrix S of the N assets 2 and then impute the variance j p qsq of individual portfolios. Wer- h h h

14 TABLE 2 Summary Statistics All Households Participants Nonparticipants Mean Median Standard Deviation Mean Median Standard Deviation Mean Median Standard Deviation Portfolio characteristics: Complete portfolio ($) ,595 12, , Risky portfolio ($) ,694 4, , Stock portfolio ($) , , Financial characteristics: Disposable income ($ per year) 26,135 20,985 28,861 30,948 26,229 34,647 18,092 15,195 10,747 Private pension premia/income (%) Financial wealth ($) 28,323 7, ,692 40,504 14, ,507 7,970 1,270 21,511 Log financial wealth Real estate wealth ($) 75,357 26, , ,983 59, ,053 29, ,507 Log real estate wealth Total liability ($) 32,156 9, ,177 40,625 16,608 98,274 18,004 2, ,139 Log total liability Retirement dummy Unemployment dummy Entrepreneur dummy Student dummy Demographic characteristics: Age Household size High school summy Post high school dummy Dummy for unavailable education data Immigration dummy Note. The table reports summary statistics of the main financial and demographic characteristics of Swedish households at the end of We convert all financial variables into U.S. dollars using the exchange rate at the end of 2002 (1 SEK p $ ). The computations are based on the random sample considered throughout the empirical analysis. Missing bank account balances are imputed using the methodology outlined in the online Appendix. All logarithms are computed in the natural base and winsorized at zero.

15 household investment mistakes 721 mers (2000) has used a similar method to evaluate the properties of stock portfolios held by mutual funds. Given a benchmark portfolio, the variance-covariance matrix S allows us to estimate the beta coefficients b of the assets and thus of the household: bh p qb h. We present in table 3, panel A, the characteristics of the risky portfolios owned by households at the end of The focus on risky portfolios allows us to investigate diversification choices while controlling for differences in cash holdings. The cross-sectional distribution of the risky portfolio standard deviation j h is reported in the first row. The total risk j h has a median value of 19.5 percent per year and a seventyfifth percentile equal to 24.0 percent. Most households thus select risky portfolios with moderate standard deviations. A sizable fraction of households, however, select risky portfolios with high j h, such as 36.4 percent (ninetieth percentile) or 64.5 percent (ninety-ninth percentile). We compare these results to a diversified equity benchmark. Because Sweden is a small and open economy, it is natural to consider a diversified portfolio of global stocks. We choose the All Country World Index (henceforth world index ) compiled by Morgan Stanley Capital International (MSCI) in U.S. dollars. From the perspective of a Swedish investor, the domestic excess return on an asset or benchmark is the difference between its return in Swedish kronor and the Swedish Treasury bill rate. Since we investigate the diversification of Swedish households, all our results are presented in terms of domestic excess returns. A Swedish household that purchases the world index can adopt two alternative strategies. First, it can hold the index and bear the corresponding currency risk, earning the Swedish krona return on the index ( unhedged index ). Second, it can use currency forward or futures contracts to hedge currency fluctuations ( currency-hedged index ). Under covered interest parity, the corresponding domestic excess return in Swedish kronor equals the excess dollar return on the index over the U.S. Treasury bill rate. 10 Over the period, the MSCI world index in U.S. dollars has a mean excess return of 6.7 percent and a mean standard deviation of 14.7 percent, that is, a Sharpe ratio of 45.2 percent. Given a benchmark index B, we consider the regression e e rh,t p ah bhrb,t h,t, (1) e e where rh,tand rb,t denote, respectively, the domestic excess returns on the household portfolio and on the benchmark. Note that this regres- 10 Solnik and McLeavey (2003) provide a textbook treatment of currency risk and hedging.

16 TABLE 3 Decomposition of Risky Portfolio Volatility Cross-Sectional Distribution Mean 1st Percentile 5th Percentile 10th Percentile 25th Percentile 50th Percentile 75th Percentile 90th Percentile 95th Percentile 99th Percentile A. Total Volatility Total risk j h (%) Systematic risk Fb hfj B (%) Idiosyncratic risk j i,h (%) Idiosyncratic share 2 (j i,h/j h) (%) Beta coefficient b h B. Idiosyncratic Volatility Idiosyncratic risk j i,h (%) Asset volatility j a,h (%) Concentration C a,h (%) Asset correlation r a,h Stock share D h Note. The first column of each panel reports the sample mean of portfolio characteristics among participating households. In the next set of columns, households are sorted by their level of total risk (panel A) or idiosyncratic risk (panel B), and the mean of 500 households around the corresponding percentile is reported.

17 household investment mistakes 723 sion has a free intercept term and does not impose any asset pricing model. From this regression we obtain the variance decomposition jh p bj h B j i,h. (2) The household portfolio thus has systematic risk Fb hfj Band idiosyncratic risk j. 11 i,h We report in table 3, panel A, how the decomposition of a household s risky portfolio varies with its overall standard deviation j h. Specifically, we consider 500 households around each percentile of j h and compute the average risk characteristics of these households. For the median j h of 19.5 percent, systematic risk has a mean of 13.0 percent and idiosyncratic risk a mean of 14.4 percent. Idiosyncratic risk is thus a large determinant of the household risk exposure. The idiosyncratic variance share j j j p (3) 2 2 i,h i,h h bhjb ji,h has a mean value of 54.9 percent for households with median total risk. In other words, more than half the risk borne by a median household in its risky portfolio is uncorrelated with the benchmark. Looking across the columns of table 3, panel A, we see a U-shaped pattern in the idiosyncratic variance share. This share is high for households with very low and very high total volatility. The high share for low-volatility households occurs because these households often hold bond funds, which do not move closely with the world equity index. The final row of panel A shows how the mean beta coefficient varies with total risk. The mean b h grows monotonically with j h and equals 0.89 for households with median total risk. B. Contributors to Idiosyncratic Risk We next analyze the idiosyncratic volatility of a household risky portfolio. As in equation (1), let h,t denote the regression residual of the portfolio N on the benchmark. We have h,t p np1 qn,h n,t, where n,t is the residual in a regression of asset n on the benchmark. We consider a stylized symmetrical model in which the residuals of all assets in a household s 2 portfolio have the same variance j and the same correlation r with a,h 11 Equation (2) imposes an adding-up constraint across estimates of systematic, idiosyncratic, and total variance. This constraint is automatically satisfied for sample variances if all assets in the household portfolio are observed over the same period of time, together with the benchmark portfolio. In practice, however, some assets are observed for shorter periods than others. In table 3, panel A, we present risk estimates that satisfy (2) by first calculating idiosyncratic and systematic variance and then adding the two to estimate total variance. a,h

18 724 journal of political economy each other. The variance of the portfolio idiosyncratic component satisfies 2 2 ji,h p j a,h[c a,h (1 C a,h)r a,h], (4) N 2 where Ca,h p np1 qn,h is a measure of the concentration of the portfolio. Let c denote the average value of ln C in the population, and C a a,h a p exp (c ). A log linearization of (4) around r p 0 and c pc implies a ( ) ln (j i,h) ln (j a,h) ln (C a,h) 1 r a,h. (5) 2 2 C a a We can ask whether households that take a lot of idiosyncratic risk typically do so (a) by picking volatile assets, (b) by holding a concentrated portfolio, or (c) by picking correlated assets. Panel B of table 3 presents a simple empirical analysis of this decomposition. The cross-sectional R of the decomposition (5) is 98 percent. 2 Portfolios are sorted by their idiosyncratic risk, and we calculate mean portfolio characteristics for 500 households around each percentile of the idiosyncratic risk distribution. The first row reports idiosyncratic risk, the second row reports the average idiosyncratic volatility of individual assets in the portfolio, the third row reports the concentration of the portfolio, and the fourth row reports the average correlation of assets in the portfolio. The main influence on idiosyncratic risk is clearly the average idiosyncratic volatility of the assets in the portfolio, which increases monotonically with idiosyncratic risk. Concentration is U-shaped in idiosyncratic risk, whereas asset correlation is hump-shaped. Households with low idiosyncratic risk often hold concentrated portfolios of mutual funds, whereas households with high idiosyncratic risk hold concentrated portfolios of individual stocks. In the middle of the idiosyncratic risk distribution, households hold diversified portfolios of mutual funds and stocks that may tend to be more correlated with one another. In support of this interpretation, the last row of the table shows that the share of direct stockholdings in the risky portfolio increases strongly with the level of idiosyncratic risk. These results show that in order to assess diversification at the household level, it is essential to observe holdings of mutual funds. The concentration of the stock portfolio, a statistic emphasized by Blume and Friend (1975) and Kelly (1995), is meaningless without a complete picture of the remaining constituents of the portfolio.

19 household investment mistakes 725 C. Estimating the Mean Returns of Household Portfolios Expected asset returns are notoriously difficult to estimate, and we have only short samples of data available for some of the stocks and mutual funds held by Swedish households. The median annual standard deviation for a single stock in our sample is 55 percent, and it is observed for 97 months or just over eight years. The standard error of a direct estimate of its mean return is therefore 0.55/ (97/12) p 19 percent. Given the uncertainty in this direct estimate, we instead infer the mean return vector m from an asset pricing model. Even if the asset pricing model is not exactly correct, it is likely to deliver better estimates of mean returns than the direct approach; this is an illustration of the general principle in econometrics that even false restrictions can reduce mean squared error if they reduce the variance of an estimate more than they increase its bias. The global CAPM is a natural asset pricing framework for an analysis of diversification since it captures the expected excess return due to covariance with global equity markets. We therefore assume that assets are priced on world markets in an international currency, specifically, that the CAPM holds in dollar-denominated excess returns relative to the U.S. Treasury bill: e e rj,t p br j m,t j,t. (6) e The market return r m,t is measured as the U.S. dollar return of the world e index in excess of the U.S. Treasury bill. As noted in subsection A, r m,t is also the domestic excess return of the currency-hedged world index under covered interest parity. Our use of the global CAPM therefore implies that the currency-hedged world index is mean-variance efficient from the perspective of a Swedish investor. In the online Appendix, we show that our results are robust to the use of a more general asset pricing model, the three-factor Fama-French model. We estimate m, given S, using standard procedures summarized in the online Appendix. Since the spread between the risk-free rate and the yield on bank deposits can be considered as a compensation for bank services, bank balances are assumed to earn the risk-free rate. We also assume that all money market funds earn this rate, an assumption that is consistent with the data we have on money market fund returns. We report in figure 2 a scatter plot of household portfolios in the mean standard deviation plane. In order to produce a clear picture, we plot a subsample of 10,000 randomly selected households. Figure 2A shows the risk characteristics of households stock portfolios, which

20 Fig. 2. Scatter plots of household portfolios. A, Stock portfolios. The scatter plot illustrates the mean and standard deviation of household stock portfolio returns. B, Complete portfolios. The scatter plot illustrates the mean and volatility of household complete portfolios. The mean returns are inferred from the global CAPM, in which the currencyhedged world index (empty diamond) is mean-variant efficient. The graphs are based on a random sample of 10,000 households at the end of 2002.

21 household investment mistakes 727 appear quite inefficient as found by Goetzmann and Kumar (2004). 12 Figure 2B includes households cash and mutual fund holdings and presents a more optimistic view of households risk management. Households appear much better diversified when we include their holdings of mutual funds and scale their risky asset holdings by their total financial assets rather than merely their stockholdings. In the online Appendix, we report the most widely held stocks and mutual funds in our entire database of all Swedish households. For individual stocks, we eliminate households that hold more than $5 million in a single stock. This procedure filters out large insider holdings and enables us to focus on popular stocks. The telecommunications company Ericsson is the most widely held stock in Sweden. It is directly owned by almost half of direct investors, and its share of direct stockholdings (8.6 percent) is considerably larger than its value share of the Swedish index (5.2 percent). Other popular stocks include telecommunications companies (TeliaSonera), fashion companies (Hennes and Mauritz), paper manufacturers (Svenska Cellulosa), pharmaceuticals (Astra Zeneca and Pharmacia), and banks (SEB, SHB, and Förenings Savings Bank, or FSB). There is also a Finnish stock (Nokia). These stocks are well-known household names, but they have relatively low Sharpe ratios averaging 17 percent. The 10 most popular funds are characterized by considerably higher Sharpe ratios, averaging 30 percent. They are sold by a few large banks: the aforementioned SEB, SHB, and FSB, along with Nordea. We note that most of them are internationally diversified. With the exception of SEB Sverige, each fund holds more than 25 percent of its assets in international securities. The most widely held fund (FSB/Robur Kapitalinvest) contains 54 percent of international stocks, and the second most popular fund (Nordea Futura) holds 17 percent in foreign stocks and 33 percent in foreign bonds. These numbers suggest that popular mutual funds enable Swedish households to achieve reasonable levels of international diversification. None of these funds, however, hedges for currency risk. It is thus considerably easier for Swedish households to hold portfolios with the efficiency of the unhedged world index than to hold portfolios that are comparable to the hedged world index. D. Mean-Variance Measures of Diversification We now provide a detailed quantitative assessment of the losses that households incur from suboptimal diversification. The moments of all 12 One popular combination of Swedish stocks is visible in this figure. Many Swedish investors directly hold both Ericsson and TeliaSonera, a telecommunications stock that was widely promoted in a privatization. The resulting two-stock portfolios form a hyperbola visible at the right of fig. 2A.

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